Related papers: Free Extensions and Jordan type

There are Jordan analogues of annihilators in Jordan algebras which are called Jordan annihilators. The present paper is devoted to investigation of those Jordan algebras every Jordan annihilator of which is generated by an idempotent as an…

The free product of an arbitrary pair of finite hyperfinite von Neumann algebras is examined, and the result is determined to be the direct sum of a finite dimensional algebra and an interpolated free group factor $L(\freeF_r)$. The finite…

J{\'o}nsson and Tarski's notion of the perfect extension of a Boolean algebra with operators has evolved into an extensive theory of canonical extensions of lattice-based algebras. After reviewing this evolution we make two contributions.…

In this paper, we show that a map $\delta$ over a triangular ring $\mathcal{T}$ satisfying $\delta(ab+ba)=\delta(a)b+a \tau(b)+\delta(b)a+b\tau(a)$, for all $a,b\in \mathcal{T}$ and for some maps $\tau$ over $\mathcal{T}$ satisfying…

We study the conformal groups of Jordan algebras along the lines suggested by Kantor. They provide a natural generalization of the concept of conformal transformations that leave 2-angles invariant to spaces where "p-angles" can be defined.…

Let k be an algebraically closed field of characteristic p \ge 0. We shall consider the problem of finding out a Jordan canonical form of J(\alpha,s) \otimes_{k} J(\beta,t), where J(\alpha,s) means the Jordan block with eigenvalue \alpha…

We describe the variety of Jordan superalgebras of dimension $4$ whose even part is a Jordan algebra of dimension $1$ or $3$. We prove that the variety is the union of Zariski closures of the orbits of $11$ and $21$ rigid superalgebras,…

The Jordan algebra of the symmetric matrices of order two over a field $K$ has two natural gradings by $\mathbb{Z}_2$, the cyclic group of order 2. We describe the graded polynomial identities for these two gradings when the base field is…

In this paper we construct 16 free algebras of modular forms on symmetric domains of type IV for some reflection groups related to the eight lattices $A_1(2)$, $A_1(3)$, $A_1(4)$, $2A_1(2)$, $A_2(2)$, $A_2(3)$, $A_3(2)$, $D_4(2)$. As a…

Let $\mathbb{F}$ be an algebraically closed field of characteristic $0$. Given a square matrix $A \in \mathbb{F}^{n \times n}$ and a polynomial $f \in \mathbb{F}[w]$, we determine the Jordan canonical form of the formal Fr\'{e}chet…

Jordan schemes generalize association schemes in a similar way as Jordan algebras generalize the associative ones. It is well-known that association schemes of maximal rank are in one-to-one correspondence with groups (so-called thin…

We construct an explicit set of generators for the finite W-algebras associated to nilpotent matrices in the symplectic or orthogonal Lie algebras whose Jordan blocks are all of the same size. We use these generators to show that such…

Quadratic Jordan algebras are defined by identities that have to hold strictly, i.e that continue to hold in every scalar extension. In this paper we show that strictness is not required for quadratic Jordan division algebras.

The method of double extension, introduced by A.~Medina and Ph.~Revoy, is a procedure which decomposes a Lie algebra with an invariant symmetric form into elementary pieces. Such decompositions were developed for other algebras, for…

Decomposition algebras and axial decomposition algebras are classes of commutative nonassociative algebras which are generalizations of axial algebras. The classes decomposition algebras, axial decomposition al;gebras and non-primitive…

A three-dimensional polynomial algebra of order $m$ is defined by the commutation relations $[P_0, P_\pm]$ $=$ $\pm P_\pm$, $[P_+, P_-]$ $=$ $\phi^{(m)}(P_0)$ where $\phi^{(m)}(P_0)$ is an $m$-th order polynomial in $P_0$ with the…

We present a genus expansion-type expression for the expected values of products of traces of expressions involving Haar-distributed orthogonal matrices. As with other real genus expansions, nonorientable surfaces appear, in addition to the…

This work is the first step towards a description of the Gromov boundary of the free factor graph of a free product, with applications to subgroup classification for outer automorphisms. We extend the theory of algebraic laminations dual to…

We show that any order isomorphism between ordered structures of associative unital JB-subalgebras of JBW algebras is implemented naturally by a Jordan isomorphism. Consequently, JBW algebras are determined by the structure of their…

Building on the foundations in our previous paper, we study Segal conditions that are given by finite products, determined by structures we call cartesian patterns. We set up Day convolution on presheaves in this setting and use it to give…